Exterior stability of Minkowski spacetime with borderline decay

TL;DR

This paper proves the exterior stability of Minkowski spacetime under decay conditions that are at the borderline of minimal decay assumptions, extending recent stability results.

Contribution

It establishes the stability of Minkowski spacetime with minimal decay assumptions, pushing the boundary of known decay conditions for stability.

Findings

Exterior stability holds with borderline decay.

Extends minimal decay stability results from 2023.

Supports the robustness of Minkowski spacetime under weaker decay conditions.

Abstract

In 1993, the global stability of Minkowski spacetime was proved in the celebrated work of Christodoulou and Klainerman. In 2003, Klainerman and Nicol\`o revisited Minkowski stability in the exterior of an outgoing null cone. In 2023, the author extended the results of Christodoulou-Klainerman to minimal decay assumptions. In this paper, we prove that the exterior stability of Minkowski holds with decay that is borderline compared to the minimal decay considered in 2023.